Answer:
r ≈ 0.5
Explanation:
To find the required interest rate, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value (ending balance)
P = the principal amount (initial investment)
r = the annual interest rate (to be determined)
n = the number of times interest is compounded per year (monthly compounding means n = 12)
t = the number of years
In this case, the principal amount (P) is $4,800, the future value (A) is $7,200, the number of times interest is compounded per year (n) is 12, and the number of years (t) is 10.
Plugging these values into the formula, we have:
$7,200 = $4,800(1 + r/12)^(12*10)
Simplifying further:
1.5 = (1 + r/12)^120
To solve for r, we can take the 120th root of both sides:
(1.5)^(1/120) = 1 + r/12
Subtracting 1 from both sides:
(1.5)^(1/120) - 1 = r/12
Multiplying both sides by 12:
12[(1.5)^(1/120) - 1] = r